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Malliavin calculus for processes with jumps

Malliavin calculus for processes with jumps BOOK REVIEWS 101 7. Solomon, B.: A new proof of the closure theorem for integral currents, Indiana Univ. Math. J., 33/3, (1984), 393-418. 8. White, B.: A new proof of the compactness theorem for integral currents, Comment. Math. Helv., 64 (1989), 207-220. B. KIRCHHEIM Stefan Banach Mathematics Centre, Warsaw, Poland K. Bicheler, J.-B. Gravereaux, and J. Jacod: Malliavin Calculus for Processes with Jumps (Stochastic Monographs Vol. 2), Gordon and Breach, 1987. The core of the theory recently designated Malliavin calculus is Malliavin's own success in proving some of H6rmander's regularity results via probabilistic reason- ings. The argument is this: A semigroup on R ~, with a second-order differential operator as its generator is considered. Under some standard assumptions for the coefficients of this operator, the elements of the semigroup become integral operators whose kernels are conditional probability distributions of a family of random variables (RVS). Being parametrized by ~+, this family forms a stochastic process which is a strong solution of an Ito stochastic differential equation (SDE), driven by time and the Brownian motion. Thus, the problem, which is very important in 'pure' analysis, whether all kernels of the semigroup possess a density is equivalent to the ('stochastic') problem http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Malliavin calculus for processes with jumps

Acta Applicandae Mathematicae , Volume 23 (1) – May 1, 2004

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References (1)

Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/BF00046923
Publisher site
See Article on Publisher Site

Abstract

BOOK REVIEWS 101 7. Solomon, B.: A new proof of the closure theorem for integral currents, Indiana Univ. Math. J., 33/3, (1984), 393-418. 8. White, B.: A new proof of the compactness theorem for integral currents, Comment. Math. Helv., 64 (1989), 207-220. B. KIRCHHEIM Stefan Banach Mathematics Centre, Warsaw, Poland K. Bicheler, J.-B. Gravereaux, and J. Jacod: Malliavin Calculus for Processes with Jumps (Stochastic Monographs Vol. 2), Gordon and Breach, 1987. The core of the theory recently designated Malliavin calculus is Malliavin's own success in proving some of H6rmander's regularity results via probabilistic reason- ings. The argument is this: A semigroup on R ~, with a second-order differential operator as its generator is considered. Under some standard assumptions for the coefficients of this operator, the elements of the semigroup become integral operators whose kernels are conditional probability distributions of a family of random variables (RVS). Being parametrized by ~+, this family forms a stochastic process which is a strong solution of an Ito stochastic differential equation (SDE), driven by time and the Brownian motion. Thus, the problem, which is very important in 'pure' analysis, whether all kernels of the semigroup possess a density is equivalent to the ('stochastic') problem

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: May 1, 2004

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